In October 2013, Gallup reported 60-percent of Americans said they favor the death penalty for convicted murderers. The only time support has been lower in Gallup's research was in November 1972, when 57% were in favor. Death penalty support peaked at 80% in 1994, but it has gradually declined since then, according to their research.
Take a look at this breakdown over 80 years of polling. Gallup first asked Americans their views on the death penalty using this question in 1936, and has updated it periodically since then, including annual updates since 1999.